Connecticut political players on both sides of the aisle — including a key Lieberman ally — said the Independent who caucuses with Democrats cannot win another three-way race, as in 2006 after he lost the Nutmeg State’s Democratic primary. There is also consensus that Lieberman would struggle to win a contested primary for either party’s nomination should he ultimately decide to abandon his Independent label.

A spokeswoman for the four-term Senator last week declined to answer specific questions about her boss’s plans, saying that he is focused on the legislative work ahead and not on an election two years down the road.

But the reality is that speculation about Lieberman’s 2012 plans is already high in Connecticut and Washington, D.C., political circles. He has yet to announce whether he will run again or where his allegiance would lie.

“No one knows what Joe’s going to do. It’s the biggest mystery in Connecticut,” said John Droney, a longtime Lieberman ally and former chairman of the Connecticut Democratic Party. “But he says he’s inclined to run.”

Lieberman’s two most logical options would be to run again as an Independent or to seek the Democratic nomination and then run as an Independent if he’s unsuccessful in the primary.

He was successful in 2006 because even though he was running as an Independent he became the de facto Republican. The GOP fielded a weak candidate in Alan Schlesinger, a state lawmaker and perennial Congressional candidate, who earned just 10 percent of the vote.

“The Republican candidate this time will be supported and stronger. And any Republican who gets over 25 percent of the vote, there’s no way Lieberman can win as an Independent,” Connecticut GOP Chairman Chris Healy said, noting that the list of possible contenders includes recently defeated Senate candidate Linda McMahon, businessman Christopher Meek, former Rep. Rob Simmons and 2010 gubernatorial nominee Tom Foley, who narrowly lost.

Simmons said he is still deeply disappointed by his party’s performance in 2010, particularly in losing the contest against Sen.-elect Richard Blumenthal. Simmons was the frontrunner in that race before losing the support of the Washington establishment and his state party.

“I continue to be proud to be a Connecticut Republican. I don’t know what the future will bring,” Simmons told Roll Call on Friday, declining to rule out anything for 2012. “I will continue to seek opportunities to be of service.”

He said Lieberman, who had $1.3 million on hand as of Sept. 30, is vulnerable.

“He has a problem. He is representing a blue state in the U.S. Senate as an Independent. He is neither fish nor fowl, if you will,” Simmons said, noting that Democrats are sure to put up a quality candidate.

High on the list of Democrats to watch are Rep. Christopher Murphy and Edward Kennedy Jr., son of the late Senator and an investment banker who helped top-of-the-ticket Connecticut Democrats this cycle. Murphy has been viewed as preparing for a Senate bid since he was first elected to the House in 2006, when he knocked off Rep. Nancy Johnson (R).

“Certainly, any of our Congressional candidates have the capability of stepping up,” Connecticut Democratic Party Chairwoman Nancy DiNardo said. “But two years is a long way off, and a lot can happen. We don’t even know if [Lieberman] is running. We don’t know if he’s seeking the Democratic nomination.”

Lieberman, who is still registered as a Democrat, would have trouble in a contested primary with either party.

Just 22 percent of Connecticut voters who supported President Barack Obama in 2008 approved of Lieberman’s job performance in a survey released Oct. 30 by the Democratic firm Public Policy Polling. He was far more popular among Republicans, earning a favorable rating from 54 percent of 2008 McCain supporters.

“He won’t get the Democratic nomination. That’s controlled by those who play in deep left field,” Droney said. “The people who play in deep left field are still smarting from what happened last time. ... It’ll be payback.”

But it seems that switching parties to run as a Republican is the least practical of Lieberman’s three options. He would have to give up his Homeland Security and Governmental Affairs Committee gavel immediately, and since Republicans are still in the minority they have nothing comparable to guarantee him in the short term.

Lieberman also aided the Democratic cause in 2010, helping to make sure Democrats retained control of the chamber and thus ensuring he wouldn’t lose his gavel.

But, Droney said becoming a Republican in the near future could help him in 2012.

“He’d probably be best off running as a Republican as far as getting re-elected,” said Droney, who stays in regular contact with Lieberman and encouraged him to run as an Independent in 2006. “I’d recommend him doing it now.”

From a political standpoint, however, the fact that the 2010 race between McMahon and Blumenthal ended up being a blowout should be part of Lieberman’s calculus as well. Democrats running statewide would likely fare even better in a presidential election year.

Healy, the state GOP chairman, made it clear his party doesn’t want Lieberman even if he were interested in a switch.

“I like Joe personally. But with the exception of the issue of terrorism, he is every bit as liberal as” Sen. Chris Dodd (D-Conn.), Healy said. “I don’t anticipate him joining the Republican Party, certainly not at our invite.”

And, of course, the tea party is always watching. While Connecticut does not have a strong local movement, the national Tea Party Express is already shaping a 2012 strategy, which could include a role in the Connecticut contest.

“We view [Lieberman] the same as any other candidate. We always are supportive of those who espouse our basic core values of lower taxes, less government intrusion, putting an end to deficit spending, etc.,” Tea Party Express spokesman Levi Russell said. “If Lieberman will strongly support those positions, then we would be happy to support him whether he runs as a Dem, Republican or Independent.”